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I have two different forecasts that are produced by ARMA models using two different data samples. The difference between the two data sets is their size: one used data from 2013-2014 and another used just 2014. I want to ensemble the two forecasts together for a better result.

Are there any algorithms to do that?

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  • $\begingroup$ What's the reason you train a separate model for a specific year? Shouldn't the first model trained on both years already capture the behavior of the data? $\endgroup$ – horaceT Aug 2 '16 at 16:31
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You only have two forecasts for each future time point, which will limit what you can do.

If you are interested in the point forecasts, simply take the mean of the two point forecasts at each future point in time. (What else can you do with only two points?) If you want to be fancy, you can use a weighted average, e.g., by weighting by the AICs of the two models, but that likely won't improve accuracy much over simple unweighted averaging.

If you have more than two point forecasts for each future time period, you can do additional fancy stuff, like taking medians, or trimmed or winsorized means.

If you are interested in the full predictive densities, simply take mixtures of the predictive densities from your two models. You can again take simple unweighted mixtures, or weight them in some way. I'd again expect a simple mixture to work just as fine as more complex weighting schemes.

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  • $\begingroup$ Yours is a generic (though certainly good) advice on combining forecasts. But i wonder if OP question is a little different in that the two models carry different part of history. This approach seems to suggest he believes early history is relevant but is revealed in a different way. $\endgroup$ – horaceT Aug 2 '16 at 16:29

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